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# Derivatives and Chain Rules

## Prerequisites

Students should be able to:

- Recognize the traditional calculus notation for partial derivatives (
*i.e.,*$\partial f/\partial x$). - Calculate a partial derivative given a symbolic expression and the variable(s) to be held constant.
- Determine a total differential by zapping with d.
- Write the thermodynamic identity for both the Partial Derivative Machine and for a gas in a piston.
- Reason about the physical quantities related to the Partial Derivative Machine.

## In-class Content

- Calculating a Total Differential (SGA - 35 min)
- Upside Down Derivatives (SGA - 10 min)
- Cyclic Chain Rule (SGA - 15 min)
- Isowidth and Isoforce Stretchability (SGA - ?? min)
- Easy and Hard Derivatives (SGA - 10 min)
- Dividing by Differentials (SGA - 15 min)

- Chain Rule Diagrams (Lecture: 20 min)

- New Surfaces activity - “Squishability” of Water Vapor (SGA - 20 min)

## Homework for Energy and Entropy

- (mbTreeDiagramMath)
*Use Tree Diagrams to find chain rules.* - (mbCyclic)
*Check cyclic chain rule for realistic equation of state* - (mbParamagnet)
*Use chain rules to solve physics problem*